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Interpretable time series classification using linear models and multi-resolution multi-domain symbolic representations

Abstract

The time series classification literature has expanded rapidly over the last decade, with many new classification approaches published each year. Prior research has mostly focused on improving the accuracy and efficiency of classifiers, with interpretability being somewhat neglected. This aspect of classifiers has become critical for many application domains and the introduction of the EU GDPR legislation in 2018 is likely to further emphasize the importance of interpretable learning algorithms. Currently, state-of-the-art classification accuracy is achieved with very complex models based on large ensembles (COTE) or deep neural networks (FCN). These approaches are not efficient with regard to either time or space, are difficult to interpret and cannot be applied to variable-length time series, requiring pre-processing of the original series to a set fixed-length. In this paper we propose new time series classification algorithms to address these gaps. Our approach is based on symbolic representations of time series, efficient sequence mining algorithms and linear classification models. Our linear models are as accurate as deep learning models but are more efficient regarding running time and memory, can work with variable-length time series and can be interpreted by highlighting the discriminative symbolic features on the original time series. We advance the state-of-the-art in time series classification by proposing new algorithms built using the following three key ideas: (1) Multiple resolutions of symbolic representations: we combine symbolic representations obtained using different parameters, rather than one fixed representation (e.g., multiple SAX representations); (2) Multiple domain representations: we combine symbolic representations in time (e.g., SAX) and frequency (e.g., SFA) domains, to be more robust across problem types; (3) Efficient navigation in a huge symbolic-words space: we extend a symbolic sequence classifier (SEQL) to work with multiple symbolic representations and use its greedy feature selection strategy to effectively filter the best features for each representation. We show that our multi-resolution multi-domain linear classifier (mtSS-SEQL+LR) achieves a similar accuracy to the state-of-the-art COTE ensemble, and to recent deep learning methods (FCN, ResNet), but uses a fraction of the time and memory required by either COTE or deep models. To further analyse the interpretability of our classifier, we present a case study on a human motion dataset collected by the authors. We discuss the accuracy, efficiency and interpretability of our proposed algorithms and release all the results, source code and data to encourage reproducibility.

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Notes

  1. According to our experiments comparing single SAX vs single SFA classifiers, shown in Sect. 4.

  2. Experiments and discussion backing these statements are available in Sects. 5 and  7.

  3. http://www.timeseriesclassification.com/results.php.

  4. https://www2.informatik.hu-berlin.de/~schaefpa/weasel/.

  5. https://github.com/hfawaz/dl-4-tsc.

  6. https://github.com/astrofrog/psrecord.

  7. The error rates of mtSAX-SEQL+LR, mtSFA-SEQL+LR and mtSS-SEQL+LR were comparable, but we only discuss mtSAX-SEQL+LR here since it is also interpretable. Note that we used a default number of symbolic representations/resolutions for mtSAX-SEQL+LR (increasing the window length with a step \(\sqrt{L}\)). By increasing the number of SAX representations, we can further improve the accuracy of mtSAX-SEQL+LR, as also discussed in Sect. 5.3.

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Acknowledgements

We would like to thank the anonymous reviewers for their detailed and constructive feedback. We would also like to gratefully acknowledge the work by researchers at University of California Riverside, USA (especially Eamonn Keogh and his team) and researchers at University of East Anglia, UK (especially Tony Bagnall and his team) and their effort in collecting, updating and making available the UCR and UEA time series classification benchmarks. We want to thank all researchers in time series classification who have made their data, code and results open source and have helped the reproducibility of research methods in this area. We acknowledge financial support for this work by Science Foundation Ireland (SFI) under grant number 12/RC/2289 (Insight Centre for Data Analytics).

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Correspondence to Thach Le Nguyen or Georgiana Ifrim.

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Le Nguyen, T., Gsponer, S., Ilie, I. et al. Interpretable time series classification using linear models and multi-resolution multi-domain symbolic representations. Data Min Knowl Disc 33, 1183–1222 (2019). https://doi.org/10.1007/s10618-019-00633-3

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Keywords

  • Time series classification
  • Multi-resolution multi-domain symbolic representations
  • SAX
  • SFA
  • SEQL
  • Linear models
  • Interpretable classifier